If what I am is determined by my genes and my environment, and every part of me obeys the laws of physics, then any choice I make in life will be governed by the laws of physics. So how can anyone believe in free will?

People believe in free will to help them find meaning in life. Without free will there is no point to, for instance, religion or love. In fact if there is no free will, then there is no point to anything at all. Except possibly pleasure in whatever form you enjoy it.
It seems to me that it is probably an adaptive behavior to believe in free will. It helps us to feel empowered in life.
From our concious perspective at least there does subjectively seem to be free will.
There is however no peer reviewed evidence, that I am aware of, that free will really exists. (If you know of any please let me know)

Depends on your interpretation of Free Will. Everything about the human mind is tangable. Thoughts and emotions are all present in the form of chemicals and electrical impulses. So, if an exact copy of, say me, was made that wasn't just a clone but had every thought, feeling and emotion I ever had inside its mind (exept the knowledge that I was creating a copy!) it would BE me. So, if that copy were placed in a situation indentical (down to the movement of every atom) to one that I have been in it would respond in exactly the way I did. However, it still made the decision to do so. So, maybe we do have the freedom to decide what to do without "fate", its just in any given situation we will always take the same course of action- the one we think is best at the time.

Free will, by simple definition, merely means that you have a choice in making decisions.
The laws of physics don't impair our free will, in that, the laws of physics don't adversely affect our emotions or our thoughts.
Therefore, it can't be argued that the laws of physics prevents us from having free will. That's like saying that someone in another city driving a car impairs our free will.
It's simply illogical.
I hope this helps to answer your question!

If the premise of your question is correct - you are nothing but a collection of chemical reactions responding to environmental influences... and this IS a common philosophical perspective - then OBVIOUSLY people can and do believe in free will because their chemical reactions and environmental influences dictate it.
The vast majority of cultures and individuals in the human race believe that there is more to human existance than just random recombinations of chemical reactions responding to environmental stimuli. Most philosophies accept the notion of a spirit or soul that transcends the sum of our chemical and environmental inputs. If this philosophical position is correct, then "free will" means more than the premise of the question allows.
We may not be able to agree on what "free will" does mean, but either philosophical position (physical only or physical+metaphysical [i.e. supernatural]) allows people to reasonably believe in free will.

I am pondering and viewing this from the reverse angle. If I choose to smoke, that decision of free will has a biological/chemical impact. If I choose to become pregnant, that has a biological/chemical impact as well. If I choose to run 5 miles a day, that has a biological/chemical impact. All of those are choices. Physics allows me to make them, but I wasn't forced to choose any of these activities. I could have made alternate choices - not to smoke, not to have a child, to walk or swim or climb trees or browse Answerbag instead of running 5 miles. It is true that each choice you make is bound by physics - as far as we know if you choose to morph into a pancake you cannot physically accomplish this. But within the laws of physics you still have literally millions of choices. Choices you have made in the past may limit the future choices you have, for example, if you choose to smoke, you may be limiting your lifespan, reducing your ability to run 5 miles, and increasing your likelihood of debilitating disease. The effects of the actions you CHOSE are determined by the laws of physics.
Considering that even identical twins exhibit differences in their personal choices, and they have the same chemical/genetic imprint, it seems that we do have free will within the laws of physics - it is the consequences/results of exercising free will where the predetermination comes in. We eat too much (an act of free will), it is a given within the laws of physics that we will feel bloated and uncomfortable.
Of course genetics can indeed limit the exercise of free will, expecially if one is predisposed to particular diseases or conditions, levels of intelligence, etc. Those were choices made even before the individual was born that determined this person's genetic makeup and unfortunately this person is suffering someone else's consequences. What makes these situations so tragic is that these individuals do not have the ability to exercise all of the options available to healthy people. But it also illustrates my point by contrast -- the human race does have free will, millions of choices at any given moment, that are not impeded or predetermined by physics. We also choose, of our free will, how to view the world and how to analyze our observations. We do not have to accept the tenets by which we were raised, we do not have to be firemen because our fathers were or abusers because we were victims of abuse. We do not have a level playing field at birth and this may seem at a cursory glance to predetermine where we will end up. However there are endless stories of great accomplishment and happiness from people who had meager and horrid childhoods who rose above it. This again says to me that we do have free will. Rather than viewing genetics and physics are limiting conditions, how about viewing them as conduits or vehicles? That would be an exercise of free will and a great experiment.

Genes are strongly influenced by chemical and environmental cues, which makes genetics much less of a blueprint for human behavior than most people believe nowadays. Genes interact with each other in very, very complicated ways, and your body is constantly changing, making neural connections, etc. Genetics is not destiny. It is perhaps a vague prediction, nothing more, nothing less.
Anyone with a sibling (the closest genetic match to you without being your clone or twin) can tell you that people with the same genes and almost identical environments can turn out very differently. That's free will in action.
Think of genes as a range of possibilities that you are born with and not a strict predestination of the person you will be. Perhaps when confronted with a situation you have a range of possible responses that includes A, B, D, and E - but my range of responses in the same situation includes B, C, F and G. It's still up to us to determine our behavior in these situation, and we might have the exact same reaction even though our natural inclinations are about 75% different! Every decision you make and experience you have will build on the person you are, create new neural pathways and cause your genetic blueprint to be activated in different ways. So even though there are restraints on the choices available to you (especially through social constraints, which you haven't mentioned here) they are still your choices to make. We aren't automatons, though modern society may make us feel that way sometimes.

Very interesting question. I was about to post a similar question myself but I found yours. Personally I think that everything is indeed fixed because everything has to obey the laws of physics. I am a reductionist, or mechanist. Therefore, I don't see how real free will can exist. I think it is not really free will, but we can think about something and make a decision. That decision has always been fixed and all future decisions will also be, but we don't see that and we don't experience it as such.
This is usually where time travel hypotheses come up, but to me true time travel does not exist, notwithstanding relativity.

The logic to defuse determinism (which is what this viewpoint could be called) goes something like this: If you argue that man does not have free will, then what you're really saying is "I have no choice in what I think or do, I think there's no such thing as free will, and now I'm telling you about that thought. But since I don't have free will, you should probably just disregard my argument as a sort of mechanical phart produced by a complicated machine."
In other words, the person who argues that there is no free will deprives himself of the intellectual agency implicit in the process of attempting to establish truth. The argument is self-defeating. So its either false, or irrelevant. If its false, we can stop discussing it. If its irrelevant, we can stop discussing it. Case closed.

First of all, a person can believe in free will as well as in anything. There were people who believed the world is flat. As of today, there are people who believe in God or gods, people who believe there is no god at all, and people who believe we can never know the answer. Some of these people are philosophers and spend their lives thinking carefully, trying to make their beliefs reasonable. The no-brainer answer is that we can believe in anything, including free will within a determined life.
Your question may go deeper than that: how do people, especially those who believe in genetic and environmental determinism, justify the belief in free will?
Just as Thom64 mentioned, many scientists (neurologists) believe that the contents of our thoughts are chemicals with electrical charges. This theory does not rule out the possibility that any person can believe in contradicting statements, such as that free will exists and yet at the same time we are genetically and environmentally determined.
But suppose we are careful thinkers: can we still justify free will, given that we are genetically and environmentally determined? I think we can.
Here I want to make a distinction between what is reality and what is experienced by a person. We are finite beings and are not omniscient. Let’s assume that a rational person believes in a life determined by all external and biological factors. But the content of the determined life remains unknown to that person. That person does not know what lies in his future, but his experience reveals that the act of willing is followed by event that is somehow evidently related to the content of the will. From the relatedness of the event and the will this person makes the connection between the two, that the act of willing causes the event afterward. The act of willing helps a person to anticipate the future, whereas the knowledge that one’s life is already determined lacks any pragmatic content. The knowledge of determinism cannot help a person navigate through his immediate choices, whereas willing seems to influence the future. Within this limited framework of personal experience, therefore, free will is justifiable.
Kai-Bong Chan

So, someone such as myself who has suffered from extreme depression because of chemical imbalances not of my choosing, has the same level of "free will"? Because of my illness my decisions have been marred to the point where I have tried to kill myself. On medication my perspectives are changed and I now don't choose to die. I think the whole notion of free will is something that was created by religious zealots to justify why people should choose to be good and go to heaven or choose to be bad and go to hell! However, the laws of physics are a myth - there are no such things. What are called the laws of physics are in fact a collection of conclusions drawn from observations and calculations of the natural and logical worlds. As such they are provisional and contingent. It is an extraordinarily arrogant of mankind to say that his superficial observations are some kind of universal laws. I don't know if I do believe in free-will, but I know that I experience life as though I have it, to at least some degree.

As a human how can I say for sure that I have free will? For all I know what I perceive to be the freedom to do and think whatever I like may be chemically induced by my brain. So to answer your question; You can believe in free will but you cant determine as to why you do.

Look at it this way: if you decide not to make any choices for yourself then someone else will choose for you. Are you OK with that? "Free will" comes only from God wanting us to choose to worship God on our own rather than because we have to.

I don't necessarily think a person is determined by genes and environment. Genes will have an effect on your outward appearance and environment will have you learn what it means to live in certain places with your certain outward appearance but every part of you does not obey the laws of physics. Your emotions, your thoughts, your habits, your preferences, etc.. do not rely on the laws of physics.

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